So, let's say we have a spacecraft in deep space. It activates its rocket engines, to keep it simple. The engine reaction channels exhaust through the aft nozzle, right? How does that chemical reaction actually induce a change in the velocity of the spacecraft? The particles have to push against the geometry of the spacecraft to provide a force. Do they do that and how when their direction vector clearly goes away from the spacecraft?

And here's something else. A pressurized spacecraft opens up an airlock which decompresses the entire deck, would that create a small thrust for the spacecraft and how? Is it the contact hull - air as it is accelerating outwards?

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Imagine a box with fuel burning inside it creating pressure.
That pressure acts equally on all the sides of the box so no net force, no accelration, no movement.

Now remove one of the walls - what happens to the balance of forces?

Opening the door in a spacecraft is exactly the same as an engine (just with a very short life), the remaining air is still pressing against the wall opposite the door and providing a thrust in that direction.

This almost caused a disaster on the Apollo moon landing. When the lander separated from the spacecraft in lunar orbit there was some residual pressure left in the airlock between the two craft which gave the lander an unexpected extra velocity that the pilot had to correct for.